Displaying similar documents to “Foliations on the complex projective plane with many parabolic leaves”

Uniformization of the leaves of a rational vector field

Alberto Candel, X. Gómez-Mont (1995)

Annales de l'institut Fourier

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We study the analytic structure of the leaves of a holomorphic foliation by curves on a compact complex manifold. We show that if every leaf is a hyperbolic surface then they can be simultaneously uniformized in a continuous manner. In case the manifold is complex projective space a sufficient condition is that there are no algebraic leaf.

On transcendental automorphisms of algebraic foliations

B. Scárdua (2003)

Fundamenta Mathematicae

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We study the group Aut(ℱ) of (self) isomorphisms of a holomorphic foliation ℱ with singularities on a complex manifold. We prove, for instance, that for a polynomial foliation on ℂ² this group consists of algebraic elements provided that the line at infinity ℂP(2)∖ℂ² is not invariant under the foliation. If in addition ℱ is of general type (cf. [20]) then Aut(ℱ) is finite. For a foliation with hyperbolic singularities at infinity, if there is a transcendental automorphism then the foliation...

The Poincaré-Bendixson theorem and arational foliations on the sphere

Igor Nikolaev (1996)

Annales de l'institut Fourier

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Foliations on the 2-sphere with a finite number of non-orientable singularities are considered. For this class a Poincaré-Bendixson theorem is established. In particular, the work gives an answer to a problem of H. Rosenberg concerning labyrinths.

Transversely affine foliations of some surface bundles over S 1 of pseudo-Anosov type

Hiromichi Nakayama (1991)

Annales de l'institut Fourier

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We consider transversely affine foliations without compact leaves of higher genus surface bundles over the circle of pseudo-Anosov type such that the Euler classes of the tangent bundles of the foliations coincide with that of the bundle foliation. We classify such foliations of those surface bundles whose monodromies satisfy a certain condition.